Wb. Dade et He. Huppert, A BOX MODEL FOR NON-ENTRAINING, SUSPENSION-DRIVEN GRAVITY SURGES ON HORIZONTAL SURFACES, Sedimentology, 42(3), 1995, pp. 453-471
The propagation of and the deposition from a turbulent gravity current
generated by the release of a finite volume of a dense particle suspe
nsion is described by a box model. The approximate model consists of a
set of simple equations, a predetermined; depth-dependent leading bou
ndary condition and one experimentally determined parameter describing
the trailing boundary condition. It yields predictions that agree wel
l with existing laboratory observations and more complex theoretical m
odels of non-eroding, non-entraining, suspension-driven flows on horiz
ontal surfaces. The essential features of gravity-surge behaviour have
been observed and are captured accurately by the box model. These inc
lude the increased rate of downstream loss of flow momentum with incre
ased particle setting velocity, the existence of maxima in the thickne
ss of proximal deposits, and the downstream thinning of distal deposit
s. Our approximation for the final run-out distance, X(r), of a surge
in deep water is given by X(r) approximate to 3(g'(o)q(o)(3)/W-s(2))(1
/5), where g'(o) is the initial reduced gravity of the surge, q(o) the
initial two-dimensional volume, and W-s the average settling velocity
of the particles in the suspension. A characteristic thickness of the
resulting deposit is given by phi(o)q(o)/X(r), where phi(o) is the in
itial volumetric fraction of sediment suspended in the surge. Our anal
ysis provides additional insight into other features of gravity-surge
dynamics and deposits, including the potential for the thickening of c
urrents with time, the maintenance of inertial conditions and the pote
ntial for strong feedback in the sorting of particle sizes in the down
stream direction at travel distances approaching X(r). Box-model appro
ximations for the evolution of gravity surges thus provide a useful st
arting point for analyses of some naturally occurring turbidity surges
and their deposits.